Home
Class 11
PHYSICS
A particle of mass m is located in a reg...

A particle of mass m is located in a region where its potential energy `[U(x)]` depends on the position x as potential Energy `[U(x)]=(1)/(x^2)-(b)/(x)` here a and b are positive constants…
(i) Write dimensional formula of a and b
(ii) If the time perios of oscillation which is calculated from above formula is stated by a student as `T=4piasqrt((ma)/(b^2))`, Check whether his answer is dimensionally correct.

Text Solution

Verified by Experts

(i) `[a]=[Ux^(2)]=ML^(2)T^(-2)L^(2)=[ML^(4)T^(-2)], [b]=[Ux]=ML^(2)T^(-2)L=[ML^(3)T^(-2)]`
(ii) `T=4 pi a sqrt((ma)/b^(2))=4 pisqrt((ma^(3))/b^(2))`, Dimension of `RHS=[4pisqrt((ma^(3))/b^(2))]=sqrt((MM^(3)L^(12)T^(-6))/(M^(2)L^(6)T^(-4))) ne T`
So, his answer is dimensionally incorrect
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MISCELLANEOUS

    ALLEN|Exercise Part -II Example Some worked out Examples|1 Videos

  • MISCELLANEOUS

    ALLEN|Exercise Exercise-01|87 Videos

  • MISCELLANEOUS

    ALLEN|Exercise SUBJECTIVE QUESTION|9 Videos

  • KINEMATICS (MOTION ALONG A STRAIGHT LINE AND MOTION IN A PLANE)

    ALLEN|Exercise BEGINNER S BOX-7|8 Videos

  • PHYSICAL WORLD, UNITS AND DIMENSIONS & ERRORS IN MEASUREMENT

    ALLEN|Exercise EXERCISE-IV|8 Videos

Similar Questions

Explore conceptually related problems

A particle of mass m is located in a one dimensional potential field where potential energy of the particle has the form u(x) = a/x^(2)-b/x) , where a and b are positive constants. Find the period of small oscillations of the particle.

The energy E of a particle at position x at time t is given by E=a/(t(b+x^(2)) Where a and b are constants. The dimensional formula of a is

Knowledge Check

  • A particle of mass m is located in a one dimensional potential field where potential energy of the particle has the form U (x) = (a)/(x^(2)) - (b)/(x) where a and b are positive constants. The position of equilibrium is:

    A
    `(b)/(2a)`
    B
    `(2b)/(a)`
    C
    `(a)/(b)`
    D
    `(2a)/(b)`

  • A particle of mass m is present in a region where the potential energy of the particle depends on the x-coordinate according to the expression U=(a)/(x^2)-(b)/(x) , where a and b are positive constant. The particle will perform.

    A
    oscillatory motion but not simple harmonic motion about its mean position for small displacements
    B
    simple harmonic motion with time period `2pisqrt((8a^2m)/(b^4))` about its mean position for small displacements
    C
    neither simple harmonic motion nor oscillatory about its mean position for small displacements
    D
    none of the above

  • A particle located in a one-dimensional potential field has its potential energy function as U(x)=(a)/(x^4)-(b)/(x^2) , where a and b are positive constants. The position of equilibrium x corresponds to

    A
    (a) `(b)/(2a)`
    B
    (b) `sqrt((2a)/(b))`
    C
    (c) `sqrt((2b)/(a))`
    D
    (d) `(a)/(2a)`

    • Similar Questions

    Explore conceptually related problems

    A partical of mass m is located in a unidimensionnal potential field where potentical energy of the partical depends on the coordinates x as U (x) = (A)/(x^(2)) - (B)/(x) where A and B are positive constant. Find the time period of small oscillation that the partical perform about equilibrium possition.

    Solve the foregoing problem if the potential energy has the form U(x)=a//x^(2)-b//x, , where a and b are positive constants.

    The potential energy of a particle depends on its x-coordinates as U=(Asqrt(x))/(x^2 +B) , where A and B are dimensional constants. What will be the dimensional formula for A/B?

    A particle located in one dimensional potential field has potential energy function U(x)=(a)/(x^(2))-(b)/(x^(3)) , where a and b are positive constants. The position of equilibrium corresponds to x equal to

    The potential energy U of a particle varies with distance x from a fixed origin as U = (Asqrt(x))/(x^(2)+B) where A and B are dimensional constants. The dimensional formula for AB is

    Home
    Profile